A382444 Triangle read by rows, defined by the two-variable g.f. (1 + y*x^2 + (y^2 + y)*x^3)/(1-(1+y)*x-y*x^2).

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 9, 18, 9, 1, 1, 11, 34, 34, 11, 1, 1, 13, 54, 86, 54, 13, 1, 1, 15, 78, 174, 174, 78, 15, 1, 1, 17, 106, 306, 434, 306, 106, 17, 1, 1, 19, 138, 490, 914, 914, 490, 138, 19, 1, 1, 21, 174, 734, 1710, 2262, 1710, 734, 174, 21, 1

Offset: 0

Author

F. Chapoton, Mar 25 2025

Keywords

• nonn
• tabl

Comments

Every row is symmetric.

Examples

			Triangle begins:
  [0] [1]
  [1] [1,  1]
  [2] [1,  4,   1]
  [3] [1,  7,   7,   1]
  [4] [1,  9,  18,   9,   1]
  [5] [1, 11,  34,  34,  11,   1]
  [6] [1, 13,  54,  86,  54,  13,   1]
  [7] [1, 15,  78, 174, 174,  78,  15,   1]
  [8] [1, 17, 106, 306, 434, 306, 106,  17,  1]
  [9] [1, 19, 138, 490, 914, 914, 490, 138, 19, 1]
  ...
		

Crossrefs

Similar to A008288, A103450 and A382436. Row sums are A265107.

Programs

Sage

y = polygen(QQ, 'y')
x = y.parent()[['x']].gen()
gf = (1 + y*x^2 + (y^2 + y)*x^3)/(1 - (1 + y)*x - y*x^2)
[list(u) for u in list(gf.O(11))]